Torsional chiral magnetic effect due to skyrmion textures in a Weyl superfluid 
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Ishihara, Yusuke; Mizushima, Takeshi; Tsuruta, Akihiro; Fujimoto, Satoshi

doi:10.1103/physrevb.99.024513

Cited by 16 publications

(9 citation statements)

References 69 publications

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“…The anomalous transport is a consequence of the axial gravitational NY anomaly due to the chiral Weyl fermions on an emergent Riemann-Cartan spacetime with torsion. We note that the early papers [10][11][12] and [5,49] treat the anomaly in terms of an axial gauge field ∼ ±p Fl and the tetrad e a µ , leading to the requirement Λ = 0 in saturating the anomaly [81], in contrast to [67,68]. This is distinct from the emergent spacetime (14) or considerations of other systems, where such fields contribute only to a single anomaly [69,70,72].…”

Section: Pacs Numbersmentioning

confidence: 98%

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Emergent Spacetime and Gravitational Nieh-Yan Anomaly in Chiral p+ip Weyl Superfluids and Superconductors

Nissinen

2020

Phys. Rev. Lett.

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Momentum transport is anomalous in chiral p + ip superfluids and superconductors in the presence of textures and superflow. Using the gradient expansion of the semi-classical approximation, we show how gauge and Galilean symmetries induce an emergent curved spacetime with torsion and curvature for the quasirelativistic low-energy Majorana-Weyl quasiparticles. We explicitly show the emergence of the spin-connection and curvature, in addition to torsion, using the superfluid hydrodynamics. The background constitutes an emergent quasirelativistic Riemann-Cartan spacetime for the Weyl quasiparticles and they satisfy the conservation laws associated with local Lorentz symmetry, restricted to the plane of uniaxial anisotropy of the superfluid (or -conductor). Moreover, we show that the anomalous Galilean momentum conservation is a consequence of the gravitational Nieh-Yan (NY) chiral anomaly the Weyl fermions experience on the background geometry. Notably, the NY anomaly coefficient features a non-universal ultraviolet cut-off scale Λ, with canonical dimensions of momentum. Comparison of the anomaly equation and the hydrodynamic equations suggests that the value of the cut-off parameter Λ is determined by the normal state Fermi liquid and non-relativistic uniaxial symmetry of the p-wave superfluid or superconductor. PACS numbers:Introduction. -Topological phases can be classified in terms of quantum anomalies that are robust to interactions and other perturbations [1-3]. Protected emergent quasi-relativistic fermi excitations coupled to gauge fields and geometry arise as dictated by topology and anomaly inflow [4][5][6]. In particular gapless fermions with Weyl spectrum and chiral anomalies are a recent prominent example [7][8][9][10][11][12][13][14][15][16]. On the other hand, topological phases and their coupling to geometry (and gravity) is currently a rapidly advancing subject. The well-established results concern the Hall viscosity [17] and chiral central charge [18][19][20] related to gravitational anomalies [21][22][23] and thermal transport in quantum Hall systems, topological superfluids (SFs) and superconductors (SCs), as well as semimetals [24-48, 66, 72, 83], the case of SFs and SCs being especially important due to the lack of conserved charge. Any purported topological response of geometrical origin is necessary more subtle than that based on gauge fields with conserved charges due to the inherent dichotomy between topology and geometry.Topologically protected Weyl quasiparticles arise also in three-dimensional chiral p-wave SFs and SCs [5,49]. As any chiral fermion in three dimensions, they suffer from the chiral anomaly in the presence of non-trivial background fields, now as an anomaly where momentum is transferred from the order parameter fluctuations to the quasiparticles [49-55],

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Section: Pacs Numbersmentioning

confidence: 98%

“…66. Related recent work discusses emergent tetrads, gauge fields and anomaly terms in Weyl SFs [67,68] and semimetals [69][70][71][72][73][74], without the framework of emergent conservation laws and geometry.…”

Section: Pacs Numbersmentioning

confidence: 99%

Emergent Spacetime and Gravitational Nieh-Yan Anomaly in Chiral p+ip Weyl Superfluids and Superconductors

Nissinen

2020

Phys. Rev. Lett.

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“…(4) has far-reaching physical consequences. Here we focus on the torsion-induced effects which have attracted significant attention recently [3,[5][6][7][8][24][25][26][27][28][29][30][31][32][33][34]. It has been shown that the torsion gives a contribution to the chiral anomaly [2] through the Nieh-Yan term [35], which in the absence of spin connection reads…”

Section: Introduction-mentioning

confidence: 99%

Topological magnetotorsional effect in Weyl semimetals

Liang

Ojanen

2020

Phys. Rev. Research

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In this work we introduce a thermal magnetotorsional effect (TME) as a novel topological response in magnetic Weyl semimetals. We predict that magnetization gradients perpendicular to the Weyl node separation give rise to temperature gradients depending only on the local positions of the Weyl nodes. The TME is a consequence of magnetization-induced effective torsional spacetime geometry and the finite temperature Nieh-Yan anomaly. Similarly to anomalous Hall effect and chiral anomaly, the TME has a universal material-independent form. We predict that the TME can be observed in magnetic Weyl semimetal EuCd2As2.

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“…Since the spin current is determined by the components of the axial current, we also note that switching on the spin connection is equivalent to switching on certain components of an axial background field A 5 . In particular we consider the response to the spin connection (14) this has the same effect as switching on the axial gauge field perturbations δA 5 z , δA 5 t . The response can therefore be expressed as…”

Section: Derivation Of Kubo Formulasmentioning

confidence: 99%

“…In materials, however, torsion does exist in the form of e.g. dislocations, and has been discussed in the context of Weyl semimetals [4][5][6][7][8][9][10], topological insulators [4,11,12], graphene [13], or Helium-3 [14]. Recently, there has been an increasing interest in condensed matter in what has been called (perhaps misleadingly) torsional (or Nieh-Yan) anomaly [4,12,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

On chiral responses to geometric torsion

Ferreiros,

Landsteiner

2020

Preprint

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We show that geometric torsion does not lead to new chiral dissipationless transport effects.Instead apparent response to torsion can be viewed as a manifestation of the chiral vortical effect.We do however find a new dissipationless transport coefficient to curvature. In Einstein-Cartan spacetimes it can be computed by a two point function of currents to first order in derivatives. Its value is half that of the chiral magnetic conductivity.

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Torsional chiral magnetic effect due to skyrmion textures in a Weyl superfluid He3−A

Cited by 16 publications

References 69 publications

Emergent Spacetime and Gravitational Nieh-Yan Anomaly in Chiral p+ip Weyl Superfluids and Superconductors

Emergent Spacetime and Gravitational Nieh-Yan Anomaly in Chiral p+ip Weyl Superfluids and Superconductors

Topological magnetotorsional effect in Weyl semimetals

On chiral responses to geometric torsion

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